in this case clearly \(\gamma _\mathcal {A}= 1/\rho _\mathcal {A}\) .
For example the class \(\mathcal {P}\)  of planar graphs has growth constant \(\gamma _\mathcal {P}\approx 27.2269\) , and thus has radius of convergence \(\rho _\mathcal {P}=1/\gamma _\mathcal {P}\approx 0.0367\) , see [1]}. More generally, by [2]}, if \(S\)  is any given surface then the class \(\mathcal {E}^S\)  of graphs embeddable in \(S\)  has the same growth constant \(\gamma _\mathcal {P}\) . See for example [3]} for background on embeddings.
